1. Field of the Invention
The present invention relates to a method for determining an optimal resonant length, among a large number of local resonant lengths which satisfy a resonant condition, that maximizes wave intensity in a resonant structure, and more precisely, to a method for determining the optimal resonant length by which the intensity of a resonant second harmonic wave of a pump wave is maximized in a resonant device configured so that the second harmonic wave resonates in a process including the second-order nonlinear interaction, and to a method for determining the optimal resonant length by which the intensity of a converted wave is maximized in a cascaded difference frequency generation process using the resonant second harmonic wave. The present invention has been produced from the work supported by the IT R&D program of MIC (Ministry of Information and Communication)/IITA (Institute for Information Technology Advancement) [2005-S054-02, 40G Module] in Korea.
2. Discussion of Related Art
Since the optical phenomenon related to second-order nonlinearity was first discovered, a main concern has been to improve conversion efficiency in phenomenological processes. Several attempts have been made to obtain higher conversion efficiency, including the attempts to discover or synthesize a new material of high-nonlinearity structure, to perform phase matching in various ways, to fabricate a nonlinear material in a form of an optical waveguide to increase interaction in three wave mixing, or to use a resonant structure.
In a second-order nonlinear optical phenomenon, the second harmonic generation means generating an optical wave of a doubled frequency 2Wp by putting a pump wave of frequency Wp into a second-order nonlinear medium. Difference frequency generation in the phenomenon means obtaining a new converted wave of frequency Wi corresponding to a frequency difference between a signal wave of frequency Ws and the pump wave of frequency Wp through the three wave mixing based on the second-order nonlinearity (see J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light in A Nonlinear Dielectric,” Phys. Rev., vol. 127, pp. 1918-1939, 1962). The second-order nonlinear optical processes are all-optical interaction excluding electrical interaction, and in particular, the difference frequency generation process can be applied to wavelength conversion in high-speed optical communication. The converted wave generated at this time has a conjugated phase through the second-order nonlinear interaction. Accordingly, the difference frequency generation process can be also applied to dispersion compensation in the high-speed optical communication.
Meanwhile, the direct difference frequency generation is to obtain the converted wave corresponding to a difference frequency Wi (=Wp−Ws) by putting the signal wave of Ws and the pump wave of Wp directly into the second-order nonlinear medium. The cascaded difference frequency generation difference frequency generation is to obtain the converted wave of Wi (=2Wp−Ws) corresponding to a difference frequency in a cascaded way, through a simultaneous interaction between the second harmonic wave of the pump wave Wp and the signal wave Ws, after putting the signal wave and the pump wave and then generating the second harmonic wave of a doubled frequency (Wp+Wp=2Wp) (see B. Zhou, C. Q. Xu, and B. Chen, “Comparison of Difference Frequency Generation and Cascaded Based Wavelength Conversion in LiNbO3 Quasi-phase-matched Waveguides,” J. Opt. Soc. Am. B. 20, pp. 846-852, 2003). When the wavelength of the converted wave Wi is not greatly different from the wavelength of the incident signal wave Ws in a wavelength range for the optical communication (Wi˜Ws), the direct difference frequency generation necessarily requires a new light source corresponding to the frequency of 2Wp, while the cascaded difference frequency generation does not require another new light source corresponding to the frequency of 2Wp. Thus the cascaded difference frequency generation can instead use the same type of light source operating in the communication wavelength range for the pump wave (Wp˜Wi˜Ws).
However, in case of the cascaded difference frequency generation, when the pump wave and the signal wave pass through the nonlinear medium, the pump wave first generates the second harmonic wave through the nonlinear interaction, and then the second harmonic wave of the pump wave generates the converted wave through the nonlinear interaction with the signal wave. As such, the cascaded difference frequency generation is a sequential process (χ(2):χ(2)) using the continuous second-order nonlinear interaction. Accordingly, this process exhibits relatively low conversion efficiency, and so most of the signal wave, the pump wave, and the second harmonic wave go out together with the converted wave as they are without participating in the nonlinear interaction.
A resonant structure was devised for the reutilization of the outgoing waves as they were, in which a natural crystal medium was used so that the pump wave or the second harmonic wave might resonate in the second harmonic generation (see A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant Optical Second Harmonic Generation and Mixing,” IEEE J. Quantum Electron, vol. 2, pp. 109-124, 1966). After then, a resonator using an optical fiber ring was designed (See C. Q. Xu, K. Shinozaki, H. Okayama, and T. Kamijoh, “Three Wave Mixing using a Fiber Ring Resonator,” J. Appl. Phys., vol. 81, pp. 1055-1062, 1997). In the cascaded difference frequency generation using the resonant structure, a fiber ring resonator for resonating the pump wave was suggested for a scheme to increase the output intensity (see C. Q. Xu, J. Bracken, and B. Chen, “Intracavity Wavelength Conversion employing a MgO-doped LiNbO3 Quasi-phase Matched Waveguide and an Erbium-doped Fiber Amplifier,” J. Opt. Soc. Amer. B, vol. 20, pp. 2142-2149, 2003). Recently however, instead of resonating the pump wave, various schemes for generating the cascaded difference frequency through resonating the second harmonic wave, which was generated through the second-order nonlinear interaction, in the resonant structure were invented (see Jong-Bae Kim, Jung-Jin Kim, Min-Su Kim, and Byung-Ha Lee, “Cascaded Difference Frequency Generation Device using Resonant Structure” KR Patent No. 0568504, 2006).
A device of a resonant type shows better conversion efficiency when compared with a conventional device of a traveling-wave type through which an optical wave propagates in a single pass. This is generally because the optical wave resonating in the resonant structure increases the wave intensity by accumulation. As the device length inducing the second-order nonlinear interaction increases, the wave intensity increases due to the increased second-order nonlinear interaction, but as the device length increases, the propagation loss increase as well and thus decreases the wave intensity to some extent. Similarly, the optical wave resonating in the resonant structure can possess stronger intensity by means of accumulation, but as the resonant length gets longer, the propagation loss gets larger and thus decreases the wave intensity. Therefore, it is intuitively expected that the resonant device using the resonant structure will possess the optimal resonant length by which wave intensity is maximized, as the increase of the wave intensity due to the accumulation and the decrease of the wave intensity due to the propagation loss are properly balanced.
In a real situation, the resonant condition in the resonant structure to be discussed later is represented as 2khL+arg(r1)+arg(r2)=2πm. Here, for a given wave vector kh and reflection coefficients r1 and r2, since the integer m can in principle exist infinitely as m=0, 1, 2, 3, . . . , this implies that the resonant length L that satisfies the resonant condition can also exist discretely and infinitely. When the basic interval of the discrete resonant lengths corresponding to the given integers is calculated, it is represented as ΔL=π/kh. The basic interval is a very small value of ΔL=173.572 nm when calculated numerically by using λh=1.55/2 nm and nh=2.2357.
Since the basic interval is such an extremely small value, in view of reality, the practical length of devices satisfying the resonant condition seems almost continuous. Hence, for the observation of resonance up to now, after an arbitrary length is selected conventionally and then the resonant condition is satisfied at the selected length by dint of controlling external conditions precisely. When compared with arbitrary lengths out of the resonant condition, the resonant wave possesses the local maxima of different magnitudes at different resonant lengths, but when a large number of the local maxima corresponding to a large number of the resonant lengths are compared with one another once again, remarkably, among the local maxima there exists a global maximum corresponding to the optimal resonant length.
However, the methods concerned with the resonant structure up to now provide at most slightly better conversion efficiency, and are completely ignorant of the fact that the resonant length can be optimized. In addition, an arbitrary resonant length is selected at one's own will because there is no way of determining the optimal resonant length at all. Accordingly, in the conventional methods there is an important and serious problem in maximizing the wave intensity to be obtained by using the resonant structure effectively.